Measuring Gaussian Quantum Information and Correlations Using the Rényi Entropy of Order 2
Abstract
We demonstrate that the Rényi2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phasespace Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.
 Publication:

Physical Review Letters
 Pub Date:
 November 2012
 DOI:
 10.1103/PhysRevLett.109.190502
 arXiv:
 arXiv:1203.5116
 Bibcode:
 2012PhRvL.109s0502A
 Keywords:

 03.67.Mn;
 03.65.Ta;
 03.65.Ud;
 42.50.Dv;
 Entanglement production characterization and manipulation;
 Foundations of quantum mechanics;
 measurement theory;
 Entanglement and quantum nonlocality;
 Nonclassical states of the electromagnetic field including entangled photon states;
 quantum state engineering and measurements;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 6+5 pages, published in PRL. Typo in Eq. (1) corrected